次の計算をしなさい。 (1) $\sqrt{8} \times \sqrt{2}$ (2) $\sqrt{14} \times \sqrt{21}$ (3) $\sqrt{2} \div \sqrt{5}$ (4) $\sqrt{42} \div \sqrt{14}$

1. 問題の内容

次の計算をしなさい。

(1) $\sqrt{8} \times \sqrt{2}$

(2) $\sqrt{14} \times \sqrt{21}$

(3) $\sqrt{2} \div \sqrt{5}$

(4) $\sqrt{42} \div \sqrt{14}$

2. 解き方の手順

(1) $\sqrt{8} \times \sqrt{2}$

$\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$

$2\sqrt{2} \times \sqrt{2} = 2 \times 2 = 4$

(2) $\sqrt{14} \times \sqrt{21}$

$\sqrt{14} \times \sqrt{21} = \sqrt{2 \times 7} \times \sqrt{3 \times 7} = \sqrt{2 \times 3 \times 7 \times 7} = 7\sqrt{2 \times 3} = 7\sqrt{6}$

(3) $\sqrt{2} \div \sqrt{5}$

$\frac{\sqrt{2}}{\sqrt{5}} = \frac{\sqrt{2} \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}} = \frac{\sqrt{10}}{5}$

(4) $\sqrt{42} \div \sqrt{14}$

$\frac{\sqrt{42}}{\sqrt{14}} = \sqrt{\frac{42}{14}} = \sqrt{3}$

3. 最終的な答え

(1) 4

(2) $7\sqrt{6}$

(3) $\frac{\sqrt{10}}{5}$

(4) $\sqrt{3}$